Estimates of pseudomoments via the Stein-Chen method (Q1415857)

The compound Poisson approximations of sums of integer-valued random variables are considered. The pseudomoments are reduced to estimates in the total variation, if the initial Stein equation is repeatedly applied for the compound Poisson approximation. A slightly more general case of pseudomoments is considered, replacing \(| j-\lambda|^k\) in terms for the absolute pseudomoments by \(f(j)\cdot(j- \lambda)^k\), \(\| f\|< \infty\).